Currently the tt_content table gets its categories field by the install tool configuration value:

$GLOBALS['TYPO3_CONF_VARS']['SYS']['defaultCategorizedTables']

The problem here is that most of the content types are defined in Configuration/TCA/Overrides since #65922.

Since the Overrides for the TCA are processed after the global categories are registered (in ExtensionManagementUtility::buildBaseTcaFromSingleFiles()), most of the content types are just left out when the CategoryRegistry calls ExtensionManagementUtility::addToAllTCAtypes().